Mathematics desk
< October 16	<< Sep \| October \| Nov >>	Current desk >

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

October 17

Names of n-1 dimensional parts of Pascal's simplexes

The points in Pascal's line are simply points. (Pascal's line, the 1-dimensional version, is simply 1-1-1-1-1-1-1-1-1-1-1-1-1-1 infinitely long. The 0-dimensional version, Pascal's point, is simply the number 1.)

The lines in Pascal's triangle are rows. The triangles in Pascal's tetrahedron are layers.

What are the tetrahedrons in Pascal's pentachoron?? What are the pentachorons in Pascal's hexateron?? And so on. Georgia guy (talk) 14:59, 17 October 2024 (UTC)[reply]

While we do have an article on Pascal's simplex, it's completely unsourced and almost all the work of a single editor. So there's really no evidence that there's any kind of standard terminology for these ideas. The name "Pascal's triangle" is well-established, but higher and lower analogues not so much. The good news is that you can define your own terminology with little chance of confusing anyone by going against existing usage. I personally don't see anything wrong with using "layers" for the tetrahedron and above. In some contexts you can talk about "slices" of multidimensional objects, and that may be applicable here as well. Either way, you'd need to define your terms to be clear about what you're talking about. --RDBury (talk) 16:23, 19 October 2024 (UTC)[reply]